The angular velocity of a body changes from $6 \ rad \ s^{-1}$ to $21 \ rad \ s^{-1}$ in a time of $1.5 \ s$. If the moment of inertia of the body is $100 \ g \ m^2$,then the rate of change of angular momentum of the body is (in $N \ m$)

Two equal and opposite forces are applied tangentially to a uniform disc of mass $M$ and radius $R$ as shown in the figure. If the disc is pivoted at its centre and free to rotate in its plane,the angular acceleration of the disc is ............

$A$ circular disc of radius $2 \ m$ is rotating at $240 \ rpm$. If a torque is applied to the disc, it slows down at a rate of $\pi \ rad/s^2$. How long will it take to stop? How many revolutions will the disc complete before coming to rest?

$A$ wheel of radius $0.4 \,m$ can rotate freely about its axis as shown in the figure. $A$ string is wrapped over its rim and a mass of $4 \,kg$ is hung. An angular acceleration of $8 \,rad \,s^{-2}$ is produced in it due to the torque. Then, the moment of inertia of the wheel is $(g = 10 \,m \,s^{-2})$.

$A$ uniform rod $AB$ of length $l$ and mass $m$ is free to rotate about point $A.$ The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about $A$ is $ml^2/3$,the initial angular acceleration of the rod will be:

$A$ disc of mass $M \ kg$ and radius $R \ m$ is rotating at an angular speed of $\omega \ rad/s$ when the motor is switched off. Neglecting the friction at the axle,the force that must be applied tangentially to the wheel to bring it to rest in time $t$ is ...............